## A review of the mass measurement techniques proposed for the Large Hadron Collider

We review the methods which have been proposed for measuring masses of new particles at the Large Hadron Collider paying particular attention to the kinematical techniques suitable for extracting mass information when invisible particles are expected.

## Determining pseudoscalar meson photoproduction amplitudes from complete experiments

A new generation of complete experiments is focused on a high precision extraction of pseudoscalar meson photoproduction amplitudes. Here, we review the development of the most general analytic form of the cross section, dependent upon the three polarization vectors of the beam, target and recoil baryon, including all single-, double- and triple-polarization terms involving 16 spin-dependent observables. We examine the different conventions that have been used by different authors, and we present expressions that allow the direct numerical calculation of any pseudoscalar meson photoproduction observables with arbitrary spin projections from the Chew–Goldberger–Low–Nambu amplitudes. We use this numerical tool to clarify apparent sign differences that exist in the literature, in particular with the definitions of six double-polarization observables. We also present analytic expressions that determine the recoil baryon polarization, together with examples of their potential use with quasi-4π detectors to deduce observables. As an illustration of the use of the consistent machinery presented in this review, we carry out a multipole analysis of the γ

p→K^{+}Λ reaction and examine the impact of recently published polarization measurements. When combining data from different experiments, we utilize the Fierz identities to fit a consistent set of scales. In fitting multipoles, we use a combined Monte Carlo sampling of the amplitude space, with gradient minimization, and find a shallow χ^{2}valley pitted with a very large number of local minima. This results in broad bands of multipole solutions that are experimentally indistinguishable. While these bands have been noticeably narrowed by the inclusion of new polarization measurements, many of the multipoles remain very poorly determined, even in sign, despite the inclusion of data on eight different observables. We have compared multipoles from recent PWA codes with our model-independent solution bands and found that such comparisons provide useful consistency tests which clarify model interpretations. The potential accuracy of amplitudes that could be extracted from measurements of all 16 polarization observables has been studied with mock data using the statistical variations that are expected from ongoing experiments. We conclude that, while a mathematical solution to the problem of determining an amplitude free of ambiguities may require eight observables, as has been pointed out in the literature, experiments with realistically achievable uncertainties will require a significantly larger number.

## Constraining the initial state granularity with bulk observables in Au+Au collisions at GeV

In this paper we conduct a systematic study of the granularity of the initial state of hot and dense QCD matter produced in ultra-relativistic heavy-ion collisions and its influence on bulk observables like particle yields,

mspectra and elliptic flow. For our investigation we use a hybrid transport model, based on (3+1)D hydrodynamics and a microscopic Boltzmann transport approach. The initial conditions are generated by a non-equilibrium hadronic transport approach and the size of their fluctuations can be adjusted by defining a Gaussian smoothing parameter σ. The dependence of the hydrodynamic evolution on the choices of σ and_{T}t_{start}is explored by means of a Gaussian emulator. To generate particle yields and elliptic flow that are compatible with experimental data the initial state parameters are constrained to be σ = 1 fm andt_{start}= 0.5 fm. In addition, the influence of changes in the equation of state is studied and the results of our event-by-event calculations are compared to a calculation with averaged initial conditions. We conclude that even though the initial state parameters can be constrained by yields and elliptic flow, the granularity needs to be constrained by other correlation and fluctuation observables.

## Understanding the proton's spin structure

We discuss the tremendous progress that has been made toward an understanding of how the spin of the proton is distributed on its quark and gluon constituents. This is a problem that began in earnest 20 years ago with the discovery of the proton 'spin crisis' by the European Muon Collaboration. The discoveries prompted by that original work have given us unprecedented insight into the amount of spin carried by polarized gluons and the orbital angular momentum of the quarks.